psc design (aashto-lrfd tyu07) tutorial
DESCRIPTION
yghjjikuuTRANSCRIPT
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Prestressed Box Girder Design
Program Version Civil 2010 v1.1 Program License Registered Revision Date May 07, 2010
Unknown Load Factor
Unknown Load Factor
Unknown Load Factor
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Prestressed Box Girder Design
(AASHTO LRFD 2007)
midas Civil
Advanced Application 14
-
Prestressed Box Girder Design
Prestressed Box Girder Design
1. Overview
2. File opening and Preferences setting
3. Checking Model Data
4. Reinforcement Input
5. Performing Structural Analysis
6. PSC Section Design
7. Checking Design Results
-
ADVANCED APPLICATIONS
CONTENTS
Overview 1
Bridge Specification and Cross-Section / 2
Matreial Properties and Allowable Stress / 5
Loads / 6
Open Model file and Save 9
Check Model Data 10
Reinforcement Input 11
Construction Stage Anlysis Control & Perform Analysis 13
PSC Section Design 15
Define Design Parameters / 15
Load Combinations / 17
Modify Material Properties / 19
Select Location for PSC Design / 20
Select Location for Output / 22
PSC Segment Assignment / 24
PSC Section Deisgn / 25
Design Results 26
PSC Design Calculation / 26
Check Design Result Tables / 26
PSC Design Forces / 38
PSC Design Result Diagram / 39
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Prestressed Box Girder Design
1
Modeling
Structural Analysis
Define design parameters
Generate load combination
Modify material properties
Select location for PSC design
Perform PSC section design
Overview Design procedure for PSC section is as follows.
Fig.1 Procedure for PSC section design
There are some limitations of PSC design function in midas Civil.
1. Construction stage analysis should be performed because PSC section needs to be checked
during the construction stage and the service state.
2. PSC section design can be performed for the beam elements only. All the elements which
are on the X-Y plane are taken as Beam members and those with some inclination to X-Y
plane are designated as Column members by the midas Civil. However, these
automatically assigned member types to elements can be modified using Modify Member
Type function (Path: Design> Common Parameters> Modify member Type).
In this tutorial, we first open FSM bridge and add reinforcement. Then we will perform PSC
section design for the construction stage and the service state.
-
ADVANCED APPLICATIONS
2
Bridge specification and Cross-Section
Bridge type: 3-span continuous PSC Box Bridge (FSM)
Bridge length: L = 40.0+ 45.0 + 40.0 = 125.0 m
Bridge width: B = 8.5 m (2 lanes)
Skew : 0(No skew)
Fig. 2 Longitudinal section view Unit: m
Fig. 3 Typical cross section Unit: m
32.000
RP1
4.000
CL OF PIER
125.000
37.00040.000
L OF PIER
RP2
C
4.000
A1P2
4.000 4.000
Construction Direction Construction Joint Construction Joint
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Prestressed Box Girder Design
3
AIR
VEN
T
L=33.5
00X1
X19EA=636.5
00
L=33.5
00X1
X19EA=636.5
00
L=33.5
00X1
X19EA=636.5
00
L=33.5
00X1
X19EA=636.5
00
AIR
VEN
T
CAB
LE "
1"
- (
15.2
4m
m -
19EA)
CAB
LE "
2"
- (
15.2
4m
m -
19EA)
CAB
LE "
3"
- (
15.2
4m
m -
19EA)
CAB
LE "
8"
- (
15.2
4m
m -
19EA)
CAB
LE "
6"
- (
15.2
4m
m -
19EA)
CAB
LE "
5"
- (
15.2
4m
m -
19EA)
CAB
LE "
4"
- (
15.2
4m
m -
19EA)
CAB
LE "
7"
- (
15.2
4m
m -
19EA)
L=49.5
00X1
X19EA=940.5
00
L=49.5
00X1
X19EA=940.5
00
L=49.5
00X1
X19EA=940.5
00
L=49.5
00X1
X19EA=940.5
00
L=49.5
00X1
X19EA=940.5
00
L=49.5
00X1
X19EA=940.5
00
L=49.5
00X1
X19EA=940.5
00
L=49.5
00X1
X19EA=940.5
00
CAB
LE "
13"
- (
15.2
4m
m -
19EA)
CAB
LE "
14"
- (
15.2
4m
m -
19EA)
CAB
LE "
15"
- (
15.2
4m
m -
19EA)
CAB
LE "
16"
- (
15.2
4m
m -
19EA)
CAB
LE
"9"
- (
15.2
4m
m -
19EA)
CAB
LE "
12"
- (
15.2
4m
m -
19EA)
CAB
LE "
11"
- (
15.2
4m
m -
19EA)
CAB
LE "
10"
- (
15.2
4m
m -
19EA)
L=50.5
00X1
X19EA=959.5
00
L=50.5
00X1
X19EA=959.5
00
L=50.5
00X1
X19EA=959.5
00
L=46.5
00X1
X19EA=883.5
00
L=46.5
00X1
X19EA=883.5
00
L=46.5
00X1
X19EA=883.5
00
L=50.5
00X1
X19EA=959.5
00
L=46.5
00X1
X19EA=883.5
00
CAB
LE "
ET-6"
- (
15.2
4m
m -
12EA)
CAB
LE "
ET-5"
- (
15.2
4m
m -
12EA)
L=35.9
15X1
X12EA=430.9
80
L=35.9
15X1
X12EA=430.9
80
CAB
LE "
ET-2"
- (
15.2
4m
m -
12EA)
CAB
LE "
ET-1"
- (
15.2
4m
m -
12EA)
L=35.8
50X1
X12EA=430.2
00
L=35.8
50X1
X12EA=430.2
00
CAB
LE "
ET-3"
- (
15.2
4m
m -
12EA)
CAB
LE "
ET-4"
- (
15.2
4m
m -
12EA)
L=47.0
00X1
X12EA=564.0
00
L=47.0
00X1
X12EA=564.0
00
32.0
00
RP1
4.0
00
CL O
F P
IER
125.0
00
37.0
00
40.0
00
L O
F P
IER RP2
C
4.0
00
A1
P2
4.0
00
4.0
00
CAB
LE "
24"
- (
15.2
4m
m -
19EA)
CAB
LE "
23"
- (
15.2
4m
m -
19EA)
CAB
LE "
22"
- (
15.2
4m
m -
19EA)
CAB
LE "
21"
- (
15.2
4m
m -
19EA)
L=37.5
00X1
X19EA=712.5
00
L=37.5
00X1
X19EA=712.5
00
L=37.5
00X1
X19EA=712.5
00
L=37.5
00X1
X19EA=712.5
00
CAB
LE "
17"
- (
15.2
4m
m -
19EA)
CAB
LE "
20"
- (
15.2
4m
m -
19EA)
CAB
LE "
19"
- (
15.2
4m
m -
19EA)
CAB
LE "
18"
- (
15.2
4m
m -
19EA)
Fig
.4 T
end
on
Pro
file
U
nit
: m
Co
nst
ruct
ion
Dir
ecti
on
Co
nst
ruct
ion
Jo
int
C
on
stru
ctio
n J
oin
t
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ADVANCED APPLICATIONS
4
Fig.5 Reinforcement Unit: mm
#4 N = 19
#4
#7 #7
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Prestressed Box Girder Design
5
Material Properties and Allowable Stress
Concrete properties for superstructure
ASTM Grade: C5000
Tendon Properties
P.C Strand: 15.2 mm (0.6strand)
Yield Strength: fpy = 1600 N/mm2
Ultimate Strength: fpu = 1900 N/mm2
Cross Sectional area: Ap = 2635.3 mm2
Modulus of Elasticity: Eps = 2.0 X 105 N/mm
2
Jacking Stress: fpj = 0.7fpu = 1330 N/mm2
Curvature friction factor: = 0.3 /rad
Wobble friction factor: k = 0.0066 /m
Anchorage Slip: s = 6 mm (At the Beginning and at the End)
Check cross section dimensions of the girder (AASHTO-LRFD 5.14.2.3.10)
Check the thickness of flanges
- Top flanges:
Clear span between webs, lw = 4400 mm
Minimum thickness = 4400/30 =146.667 mm
Top flange thickness = 240 mm. OK.
- Bottom flanges:
Clear span between webs, lw = 3864 mm
Minimum thickness = 3864/30 =128.8 mm
Bottom flange thickness = 250 mm. OK.
Check whether transverse prestressing is required or not
lw = 4.400 m < 4.57 m( = 15 feet) Transverse prestressing not required.
Check web thickness
Minimum thickness, tmin = 304 mm ( = 12 inches)
Web thickness, tw = 318 mm. OK.
Check the length of top flange cantilever
The distance between centerline of the webs: ln = 4950 mm
ln X 0.45 = 2228 mm > 1500 mm. OK.
Check overall cross-section dimensions
Maximum live load plus impact deflection: 6.433 mm
Deflection limit, L/1000 = 45000/1000 = 45 mm. OK.
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ADVANCED APPLICATIONS
6
Load Dead Load
Self weight
Input Self-Weight
Superimposed dead load
w = 35.796 kN/m
Prestress
Strand (15.2 mm19 (0.6- 19))
Area: Ap = 2635.3 mm2
Duct Size: 103 mm
Prestressing force: 70 % of ultimate strength.
fpj = 0.7fpu = 1330 N/mm2
Prestressing losses after the initial loss (automatically calculated by program)
Friction Loss:)kL(
0)X(ePP
= 0.3 /rad, k = 0.006 /m
Anchorage Slip Loss: Ic = 6 mm
Elastic Shortening Loss: PE = fP.ASP
Final Loss (automatically calculated by program)
Relaxation (CEB-FIP)
Creep and Shrinkage Loss (CEB-FIP)
Creep and Shrinkage
Code: CEB-FIP (1990).
Characteristic compressive strength of concrete at the age of 28 days :
34.474 N/mm2.
Relative Humidity of ambient environment: 70%
Notational size of member: 364 mm.
Type of cement: Normal or rapid hardening cement (N, R).
Concrete age when subjected to long term loads: t0 = 5 days
Age of concrete at the beginning of shrinkage: 3 days
Air temperature or curing temperature: T = 20C
Creep Coefficient: Automatically calculated within the program
Shrinkage Coefficient: Automatically calculated within the program
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Prestressed Box Girder Design
7
Live loads
Condition
A. Vehicle Load : HL-93TDM, HL-93TRK B. Dynamic Allowance : 33%
Support Settlement
Consider each pier undergoing the support settlement of 10 mm under unfavorable
condition.
Temperature Loads
Temperature Range for Procedure A (assuming Moderate climate)
10 degree to 80 degree F
Temperature Gradient (assuming Zone 2)
-Positive temperature value
T1 = 46F
T2 = 12F
-Negative temperature value
T1 = -0.3 X 46F = -13.8F
T2 = -0.3 X 12F = -3.6F
Fig. 6 Positive Vertical Temperature Gradient
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ADVANCED APPLICATIONS
8
1.46
Wind Loads
Wind Load: 3 kN/m2
Fig. 7 Wind Load Distribution
Total Height = Section Depth + Barrier + Noise barriers = 3+1+2.5 = 6.5 m
Wind Pressure = 3 kN/m2
Wind Load = 6.5 X 3 kN/m2
= 19.5 kN/m (Horizontal Load)
= 19.5 kN/m X -1.46m = -28.47 kN.m/m (Moment)
3 kN/m2
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Prestressed Box Girder Design
9
Open model file and Save
For construction stage analysis of FSM bridge, open ( Open Project) FSM file, and then
save the file as PSC Design
File / Open Project
File / Save As(PSC Design)
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ADVANCED APPLICATIONS
10
Check the model data
In this tutorial, the effects of reinforcement has been considered for the calculation of the
section property and creep restraint.
Fig. 8 FSM model used for section check
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Prestressed Box Girder Design
11
Reinforcement Input
Enter longitudinal reinforcement, shear reinforcement and torsion reinforcement data of the
PSC section. The reinforcement data of the PSC box is as follows.
Fig. 9 Reinforcement in longitudinal direction Unit: mm
The shear/torsion reinforcement data of the PSC box is as follows.
Table 1. Shear/torsion reinforcement data
Shear reinforcement
Pitch 0.15 m
Angle 90
Alt 0.0015484 m2 (4-#7)
Torsion
reinforcement
Pitch 0.15 m
Awt 0.0003871m2 (1-#7)
Alt 0.0078554m2 (62-#4)
Lets assume that the longitudinal reinforcement, shear reinforcement, and torsion
reinforcement are same throughout the bridge.
We can enter the longitudinal reinforcement and shear reinforcement data by selecting all the
elements at a time, because there is same reinforcement throughout the bridge.
Aw is the area of vertical re-bars which are placed in the web and Awt is the area of one leg of
outermost closed stirrups (Fig. 9 ) of the closed stirrups placed towards the exterior.
Alt is the total area (Fig 9. ) of longitudinal torsion reinforcement distributed around
the perimeter of the closed stirrups.
In this tutorial, the arrangement
of longitudinal
rebars has been
simplified for
convenience.
#4
#4 N = 19
#7 #7
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ADVANCED APPLICATIONS
12
Model / Properties / Reinforcement of Section
Section List>Span
Longitudinal reinforcement
1. Dia (#4), Number (35), Ref. Y (Centriod), Y (0), Ref. Z (Top), Z (0.06),
Spacing (0.25).
2. Dia (#4), Number (19), Ref. Y (Centriod), Y (0), Ref. Z (Bottom), Z (0.06),
Spacing (0.25)
Shear Reinforcement
Diagonal Reinforcement>Pitch (0.15), Angle (90), Aw (0.0015484)
Torsion Reinforcement >Pitch (0.15), Awt (0.0003871), Alt (0.0078554)
Fig. 10 Reinforcement of PSC section
By checking on Both end parts (i
& j) have the same
reinforcement,
the reinforcement
data of one part
will be copied to
another.
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Prestressed Box Girder Design
13
Construction Stage Analysis Control & Perform Analysis
Modify Construction Stage Analysis Control Data to take into account the effect of re-bars in
creep and shrinkage restraint. In case of a PSC section, we can consider rebars for the
calculation of section properties of PSC Box.
We are now ready to perform the structural analysis.
Analysis /Construction Stage Analysis Control
Consider Re-Bar Confinement Effect (on)
Analysis / Main Control Data
Consider Reinforcement for Section Stiffness Calculation (on)
Analysis / Perform Analysis
Fig.11 Input window of the Construction Stage Analysis Control Data
Consider the reinforcement
entered into the
PSC section for
the calculation of
section properties.
If this option is
checked off, the
reinforcement will
not be considered
for calculation of
section properties.
-
ADVANCED APPLICATIONS
14
Fig.12 Main Control Data dialog box
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Prestressed Box Girder Design
15
PSC Section Design
In this tutorial, we will learn how to check the stresses and the strengths of the PSC sections,
using the analysis results.
In midas Civil, the PSC section check is performed after a series of tasks such as defining
design parameters, load combinations, modifying material properties, selecting locations for the
section check etc.
Define Design Parameters
Define the design parameters such as design standards, tendon type, bridge type, type of
construction, corrosive condition and the method to compute flexural strength of PSC box
girder.
In the case of Flexural Strength, if Code is selected, the design standard is used to
determine of flexural strength of PSC Box girder (AASHTO-LRFD, Clause 5.7.3.2). Strain
Compatibility method is provided for more precise calculation of flexural strength using strain
compatibility approach.
If the Bridge Type is Fully PSC, no crack is allowed in the PSC Box. But if Partially
PSC is selected as the Bridge Type, the user can select Exposure Factor for Crack Width
depending upon the exposure condition (AASHTO-LRFD 07, Clause 5.7.3.4).
The user can select different options in the Output Parameters depending upon the
requirement.
Design / PSC Design / PSC Design Parameters
Input Parameters
Design Code: AASHTO-LRFD 07
Tendon Type: Low Relaxation Tendons (on)
Bridge Type: Fully PSC (on)
Construction Type: Segmental (on)
Corrosive Condition: Severe (on)
Flexural Strength: Code (on)
Output Parameters
Select All
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ADVANCED APPLICATIONS
16
Fig. 13 Defining design parameter
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Prestressed Box Girder Design
17
Load Combination
We can generate load combinations for the PSC design based on Bridge Design Specification
(AASHTO LRFD 07 with 2008 interim),
In midas Civil, Auto Generation function automatically generates load combinations for ULS
and SLS according to the design standard of users requirement.
In this tutorial we will generate load combinations based on the Bridge Design Specification
(AASHTO-LRFD 07).
Result / Combination / Concrete Design/
Input parameter of the design calculation
Design Code > AASHTO-LRFD 07
Manipulation of Construction Stage Load Case> CS Only
Condition for Temperature > All Other Effects
Fig.14 Load combination using Auto Generation
If CS Only is selected, the
program
generates load
combinations after
construction stage
analysis and it
includes only
construction stage
load cases.
-
ADVANCED APPLICATIONS
18
Tendon Primary load is not included in the flexural strength check. It is because Tendon Primary is
considered while computing the nominal strength. Creep Secondary & Shrinkage Secondary are used
for member force calculation. In midas Civil, Creep & Shrinkage Primary are used for finding
displacement.
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Prestressed Box Girder Design
19
Modify material properties
This function is used to modify the properties of the steel rebar and the concrete material
defined while creating analysis model. This modification will be used only for the designing
and strength verification. The analysis results remain unaffected.
In this design example, concrete material is same i.e. C5000, we only need to specify the grades
of Main rebar i.e. longitudinal steel and sub-rebar i.e. steel used for shear reinforcement.
Design / PSC Design / PSC Design Material
Material List> ID1
Concrete Material Selection
Code>ASTM (RC)
Grade>C5000
Rebar Selection
Code> ASTM (RC)
Grade of Main Rebar>Grade 60; Grade of Sub-Rebar>Grade 60
Fig. 15 Modify concrete and steel materials for design
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ADVANCED APPLICATIONS
20
Select Locations for PSC Design
Using this function we can select the elements and their ends (only I, only J or both I & J) to be
checked for moment or shear or both, for PSC. If we do not select specific locations for check,
both parts (I&J) of all the elements will be checked for both moment and shear.
Design / PSC Design / PSC Design Option
Option>Add/Replace
Select Elements by Identifying (Element: 16, 17, 26, 27)
Moment> I &J (on)
Shear> None (on)
Select Elements by Identifying (Element: 1to2)
Moment> None (on)
Shear> I &J (on)
Fig.16 PSC Design option
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Prestressed Box Girder Design
21
We can check selected elements and locations in the Table and it is also possible to add, modify,
and delete in the Table.
In the table, delete all elements which are selected for the check.
As mentioned, if location for the moment and shear check is not specified by the user, the
program will automatically check I & J ends of all the elements.
Design / PSC Design / PSC Design Tables / PSC Design Option
Select All> Delete
Fig. 17 PSC Design Option Table
It is convenient if we select PSC
Design Option of
PSC Design from
Table Tab in Tree
View.
Delete using Delete Key in the
Keyboard
-
ADVANCED APPLICATIONS
22
Select location for output
Using this feature we can select the ends of elements for which flexural and (or) shear and (or)
torsion strength are to be produced in output report (in excel sheet) generated from PSC
Design Calculation after PSC Design. It is important to note that output can be produced only
for those elements which have been assigned PSC Design Option.
In the following example, we will print the flexure, shear and torsion strength of the elements
in the central span and at support.
Design / PSC Design / PSC Print Option
Option>Add/Replace
Select Elements by Identifying (Element: 16, 17, 26, 27, 35, 36)
Moment Strength> M (+) >I &J (on)
Moment Strength> M (-) >I &J (on)
Shear Strength>I &J (on)
Torsion Strength>I &J (on)
Fig. 18 PSC Print Option dialog box
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Prestressed Box Girder Design
23
We can check the selected elements and locations in the table and it is possible to add, modify
and delete data in the table
If no element is selected in PSC Print Option, we wont get the flexural strength, shear strength
and torsion strength of any element in the PSC Design Calculation report.
Design / PSC Design / PSC Design Tables / PSC Print Option
Fig. 19 PSC Print Option Table
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ADVANCED APPLICATIONS
24
PSC Segment Assignment
This feature enables the user to provide the location of joints for design. One segment consists
of consecutively selected elements. I and J ends of each segment are considered as joint
locations. Segment assignment is ignored if non-segmental option is selected in PSC Design
Parameters. If the modeling is such that a segment is represented by single element, then no
need to use this feature.
-
Prestressed Box Girder Design
25
PSC Section Design
Perform the PSC Design
Design / PSC Design / PSC Design
Fig. 20 Message after completing PSC Design
-
ADVANCED APPLICATIONS
26
Design Results
We can see the design results in Tables (Design->PSC Design->PSC Design Result Tables).
We can also check the design calculation in excel sheet format. This design result corresponds
to the Input and Output parameters defined in PSC Design Parameters.
PSC Design Calculation
It produces PSC design results in excel format for the elements selected in PSC Print Option.
This sheet can be generated in Post CS stage and if the number of selected elements is larger, it
takes longer time to generate the sheet.
The excel sheet is saved in the saved folder of model files (*.mcb).
Design / PSC Design / PSC Design Calculations
Check Design Result Tables
The results that can be checked have been categorized into two.
In the first category we can check the stresses at construction stages and at service load.
The second category corresponds to ultimate limit state check. Here we can perform Flexural
strength check, Shear strength check and Combined Shear & Torsion Check at factored loads.
Fig. 21 PSC design result tables
Following sign convention is used for stresses
- Compression: (+)
- Tension: (-)
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Prestressed Box Girder Design
27
1. Check Stress for Cross Section at a Construction Stage
It checks the compression and tensile stresses for cross section at a construction
stage. The checks are made as per the clauses 5.9.4.1.1 and 5.9.4.1.2 of AASHTO
LFRD-07. Max/Min stress are shown for each part (I, J) of the elements, at the
construction stages for which the stresses at that part are maximum.
Description of each item in the above table is as follows
Elem : Element No. FTL : Combined Stress due to bending
moment about major axis (My),
minor axis (Mz) and axial force at
Top Left fiber.
Part : Location(I, J) FBL : Combined Stress due to bending
moment about major axis (My),
minor axis (Mz) and axial force at
Bottom Left fiber.
Comp/Tens : Compression, Tension FTR : Combined Stress due to bending
moment about major axis (My),
minor axis (Mz) and axial force at
Top Right fiber.
Stage :Critical Construction
Stage
FBR : Combined Stress due to bending
moment about major axis (My),
minor axis (Mz) and axial force at
Bottom Right fiber.
OK :Stress check result,
whether section is ok or
Not good
FMAX : Maximum combined stress out
of the above six.
FT :Combined Stress due to
bending moment about
major axis (My) and axial
force at Top fiber.
ALW : Allowable stress of cross section
at construction stage as per
AASHTO LRFD-07 5.9.4.1.1 &
5.9.4.1.2 clause.
FB : Combined Stress due to
bending moment about
major axis (My) and axial
force at Bottom fiber.
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ADVANCED APPLICATIONS
28
2. Check Tensile Stress for Prestressing Tendons
It checks the tensile stresses for prestressing tendons. The check is made as per the clause
5.9.3 of AASHTO LRFD-07. The table presents the stresses according to Tendon Groups.
Description of each item in the above table is as follows
Tendon : Tendon profile names. AFDL1 : Allowable Stress in Tendon
immediately after anchor set at
anchorages.
FDL1 : Maximum stress in tendon along
the length of the member away
from anchorages, immediately
after anchor set..
AFDL2 : Allowable stress in tendon
immediately after anchor set
elsewhere
FDL2 : Stress in tendon immediately
after anchor set, elsewhere along
the tendon length.
AFLL1 : Allowable stress in tendon at
service limit state after losses
FLL1 : Maximum stress in tendon after
all losses at the last stage..
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Prestressed Box Girder Design
29
3. Check Stress for Cross Section at Service Loads
It checks the compression and tensile stress for cross section at service loads. This
check is made as per the clause 5.9.4.2.1 and 5.9.4.2.2 of AASHTOLRFD-07. The
table shows maximum compression and tensile stresses for each part of the
elements along with the critical load combination (causing that stress).
Description of each item in the above table is as follows
Element : Element number. FB : Combined Stress due to bending
moment about major axis (My) and
axial force at Bottom fiber
Part : Check location (I-End, J-
End) of each element.
FTL : Combined Stress due to bending
moment about major axis (My),
minor axis (Mz) and axial force at
Top Left fiber
Comp./Tens : Compression or Tension
Stress.
FBL : Combined Stress due to bending
moment about major axis (My),
minor axis (Mz) and axial force at
Bottom Left fiber
Type : Member force due to
moving load, which causes
the maximum stress.
FTR : Combined Stress due to bending
moment about major axis (My),
minor axis (Mz) and axial force at
Top Right fiber
LCom
Name
: Load Combination Name FBR : Combined Stress due to bending
moment about major axis (My),
minor axis (Mz) and axial force at
Bottom Right fiber
CHK : Combined stress check for
Service loads
FMAX : Maximum combined stress out of
the above six.
FT : Combined Stress due to
bending moment about major
axis (My) and axial force at
Top fiber.
ALW : Allowable stress in concrete at
service limit state as per AASHTO
LRFD-07 5.9.4.2.1 & 5.9.4.2.2
clause
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ADVANCED APPLICATIONS
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4. Principal Stress at Construction Stage
It checks the principal tensile stresses in the PSC section at a construction stage at which
the Sig_Max is maximum at the given element. The allowable stresses are calculated as per
table 5.14.2.3.3-1 of AASHTO-LRFD 2007.
Description of each item in the above table is as follows.
Elem : Element Number Sig_P5 : Principal stress at the top of
left web (at Z1 level).
Part : Check location (I-End, J-
End) of each element
Sig_P6 : Principal stress at the top of
right web (at Z1 level).
Comp/Tens. : Compression or Tension
Stress
Sig_P7
: Principal stress at the
neutral axis in left web (Z2
level).
Stage : Construction Stage Sig_P8 : Principal stress at the
neutral axis of right web (at
Z2 level).
CHK : Principal stress check for
construction stages
Sig_P9 : Principal stress at the
bottom of left web (at Z3
level).
Sig_P1 : Principal stress at top-left of
top flange
Sig_P10 : Principal stress at the
bottom of right web( at Z3
level)
Sig_P2 : Principal stress at top-right
of top flange
Sig_MAX : Maximum of P1-P10
Sig_P3
: Principal stress at bottom-
right of bottom flange
Sig_AP : Allowable principal tensile
stress at neutral axis in the
web
Sig_P4 : Principal stress at bottom-
left of bottom flange
The checking location (Z1 & Z3) of
the shear stress in
the web can be
specified under
Shear Check while
defining PSC
sections. And, if we
check AUTO, the
program will decide
the level Z1 and Z3
automatically.
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Prestressed Box Girder Design
31
5. Principal Stress at Service Loads (excluding Torsional Shear Stress)
It checks principal tensile stresses in the PSC section at service loads (excluding shear
stress due to torsion). The allowable stresses are calculated as per clause 5.9.4.2.2 of
AASHTO-LRFD 2007.
Description of each item in the above table is as follows
Elem : Element Number Sig_P4 : Principal stress at bottom-
left of bottom flange
Part : Principal stress check for
construction stages
Sig_P5 : Principal stress at the top of
left web (at Z1 level).
Comp/Tens. : Compression or Tension
Stress
Sig_P6
: Principal stress at the top of
right web (at Z1 level).
LCom.
Name
: Load combination name Sig_P7
: Principal stress at the
neutral axis in left web (Z2
level).
Type : Member force due to
moving load, which causes
the maximum stress.
Sig_P8 : Principal stress at the
neutral axis of right web (at
Z2 level).
CHK : Principal stress check for
service loads at maximum
shear force.
Sig_P9 : Principal stress at the
bottom of left web (at Z3
level).
Sig_P1 : Principal stress at top-left of
top flange
Sig_P10 : Principal stress at the
bottom of right web( at Z3
level)
Sig_P2 : Principal stress at top-right
of top flange
Sig_MAX : Maximum of P1-P10
Sig_P3 : Principal stress at bottom-
right of bottom flange
Sig_AP : Allowable principal tensile
stress at neutral axis in the
web
The elements, for which the
stress value is
higher than the
allowable stress,
are shown in red
colour.
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ADVANCED APPLICATIONS
32
6. Principal stress at service loads
It checks principal tensile stresses at service loads.
Description of each item in the above table is as follows.
Elem : Element Number Sig_P4 : Principal stress at bottom-
left of bottom flange
Part : Principal stress check for
construction stages
Sig_P5 : Principal stress at the top of
left web (at Z1 level).
Comp/Tens. : Compression or Tension
Stress
Sig_P6
: Principal stress at the top of
right web (at Z1 level).
LCom.
Name
: Load combination name Sig_P7
: Principal stress at the
neutral axis in left web (Z2
level).
Type : Member force due to
moving load, which causes
the maximum stress.
Sig_P8 : Principal stress at the
neutral axis of right web (at
Z2 level).
CHK : Principal stress check for
service loads at maximum
shear force.
Sig_P9 : Principal stress at the
bottom of left web (at Z3
level).
Sig_P1 : Principal stress at top-left of
top flange
Sig_P10 : Principal stress at the
bottom of right web( at Z3
level)
Sig_P2 : Principal stress at top-right
of top flange
Sig_MAX : Maximum of P1-P10
Sig_P3 : Principal stress at bottom-
right of bottom flange
Sig_AP : Allowable principal tensile
stress at neutral axis in the
web
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Prestressed Box Girder Design
33
7. Check Flexural Strength
It checks and compares flexural strength of the PSC section against the factored moment.
Flexural strength is calculated as per the clause 5.7.3.2 of AASHTO LRFD-07, given by
the formula:
=
2 +
2
2 + 0.85
22
The rebars in the compression zone are also considered for the calculation of flexural
strength. Depending upon the users input in PSC Design Parameters for flexural strength,
strain compatibility method can also be used for precise calculation of flexural strength.
Description of each item in the above table is as follows.
Elem : Element number Muy : Factored moment acting at
section about y axis
Part : Check location (I-End, J-
End) of each element.
Mcr : Cracking moment of the
section
Positive/
Negative
: Positive/Negative Moment Mny : Nominal moment of resistance
of section about y axis
LCom
Name
:Load combination name
corresponding to maximum
and minimum value
PhiMny : Factored moment of resistance
of section about y axis. (Phi
assumed as 1.0)
Type : Member force due to
moving load, which causes
the maximum stress.
PhiMny
/1.33Mu
y
:Ratio of factored moment of
resistance to 1.33 times factored
moment acting on the section
about y axis
CHK : Flexural strength check for
element.
PhiMny
/1.2Mcr
: Ratio of factored moment of
resistance to 1.2 times cracking
moment of the section.
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ADVANCED APPLICATIONS
34
8. Check Shear Strength
It checks the shear strength of the PSC section. Shear resistance is computed as per the
section 5.8 of AASHTO LRFD-07.
Shear stress on concrete is determined by:
= lVu Vp l
Nominal Shear resistance is calculated as:
i) For post-tensioned segmental box girder bridges:
Vn is given by lesser of the two (Clause 5.8.6.5):
1. = +
where,
= 0.0632
= cot + cot sin
2. = 0.379
Note: Check for appropriate concrete section dimension (Eq. 5.8.6.5-5, AASHTO-LRFD
07) is not done as this doesnt correspond to strength of the section.
ii) For non-segmental bridges:
Vn is given by lesser of the two (Clause 5.8.3.3):
1. = + + where,
= 0.0316
2. = 0.25 +
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Prestressed Box Girder Design
35
Description of each item in the above table is as follows.
Elem : Element number de :Effective depth from extreme
compression fiber to centroid of
the tensile force in the tensile
reinforcement
Part : Check location (I-End, J-End)
of each element
dv :Effective shear depth
Max/Min : Maximum shear, minimum
shear
ex :Longitudinal strain in the web of
the member
LCom
Name
:Load combination name
corresponding to maximum
and minimum value
theta :Angle of inclination of diagonal
compressive stresses
Type : Member force due to moving
load, which causes the
maximum stress.
beta :Factor relating effect of the
longitudinal strain on the shear
capacity of the concrete, as
indicated by the ability of
diagonally cracked concrete to
transmit tension
CHK : Shear strength check for
element.
Avs :Area of transverse reinforcement
within distance s
Vu : Factored shear at section Ast :Total area of longitudinal mild
steel reinforcement
Mu :Factored moment at the
section
Al :Area of longitudinal torsion
reinforcement in the exterior web
of the box girder
Vn :Nominal shear resistance at
section
bv :Width of web adjusted for the
presence of ducts
Phi :Resistance Factor Avs_min :Minimum area of the transverse
reinforcement required within
distance s
Vc :Nominal shear resistance of
concrete
Avs_reqd :Area of transverse reinforcement
required within distance s
Vs : Shear resistance provided by
transverse (shear)
reinforcement.
Al_min :Minimum area of longitudinal
torsion reinforcement in the
exterior web of the box girder
required
Vp :Component of the effective
prestressing force in the
direction of applied shear,
positive if resisting shear
bv_min :Minimum width of the web
adjusted for the presence of the
ducts required
PhiVn :Factored shear resistance
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ADVANCED APPLICATIONS
36
9. Check Combined Shear and Torsion Strength
It checks the combined shear and torsion strength of the PSC section. Combined Shear and
Torsion check is done as per Clause 5.8.6.4 for Segmental box girder bridges and Clause
5.8.3.6.2 for other bridges.
Nominal torsional resistance, =20
cot
Area of additional longitudinal reinforcement, =
20
Description of each item in the above table is as follows.
Elem : Element number Phi-tTn : Factored torsional resistance
Part : Check location (I-End, J-
End) of each element
de :Effective depth from extreme
compression fibre to centroid of
the tensile force in the tensile
reinforcement
Max/Min :Maximum/Minimum
torsion/shear
dv :Effective shear depth
LCom
Name
:Load combination
corresponding to maximum
and minimum value
ex :Longitudinal strain in the web
of the member
Type : Member force due to
moving load, which causes
the maximum stress.
theta :Angle of inclination of diagonal
compressive stresses
CHK : Shear strength check for
element.
beta :Factor relating effect of the
longitudinal strain on the shear
capacity of the concrete, as
indicated by the ability of
diagonally cracked concrete to
transmit tension
Vu : Factored shear at section Avs :Area of transverse
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Prestressed Box Girder Design
37
reinforcement within distance s
Tu : Factored torsional moment
at section.
Ast :Total area of longitudinal mild
steel reinforcement
Mu :Factored moment at the
section
Al :Area of longitudinal torsion
reinforcement in the exterior
web of the box girder
Vn :Nominal shear resistance at
section
bv :Width of web adjusted for the
presence of ducts
Tn : Nominal torsional resistance
at section.
Avs_min :Minimum area of the transverse
reinforcement required within
distance s
Phi :Resistance Factor Avs_reqd :Area of transverse
reinforcement required within
distance s
Phi-t : Resistance factor for
torsion.
Al_min :Minimum area of longitudinal
torsion reinforcement in the
exterior web of the box girder
required
Vc :Nominal shear resistance
provided by tensile stresses in
concrete
bv_min :Minimum width of the web
adjusted for the presence of the
ducts required
Vs :Shear resistance provided by
shear stresses in concrete
At :Total area of transverse torsion
reinforcement in the exterior
web of cellular members
Vp :Component in the direction
of applied shear of the
effective prestressing force,
positive if resisting shear
At_req :Total area of transverse torsion
reinforcement in the exterior
web of cellular members
required
PhiVn :Factored shear resistance
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ADVANCED APPLICATIONS
38
PSC Design Forces
This feature returns the design forces for each element under different load combination in
spreadsheet format table. The table shows concurrent member forces namely Fx, Fy, Fz, Mx,
My and Mz for all the elements under all load combinations.
Design / PSC Design / PSC Design Forces
Description of each item in the above table is as follows.
Elem : Element number Fy : Design Shear force at the
element end along y axis
Part : Check location (I-End, J-
End) of each element
Fz : Design Shear force at the
element end along z axis
LCom
Name
: Load Combination
corresponding to maximum
and minimum value
Mx : Design torsional moment at
the element end
Type : Member force due to
moving load, which causes
the maximum stress.
My : Design moment at the element
end due to bending about y axis.
Fx : Design axial force at the
element end
Mz : Design moment at the element
end due to bending about z axis.
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Prestressed Box Girder Design
39
PSC Design Result Diagram This feature enables users to check result diagrams in contours. We can see the member force
diagrams along with the nominal strength diagram.
Design / PSC Design / PSC Design Result Diagram
Load Cases/Combinations> All COMBINATION
Option>Force
Components> Flexure-y
Max, Min
Diagram Option
Scale Factor > 2
Fill Type > Solid
Fig. 22 PSC Design Result Diagram Dialog
There is only All COMBINATION in
case of PSC
If Safety factor is chosen, the program
displays the ratio
diagram of design
forces to strengths.
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ADVANCED APPLICATIONS
40
Fig. 23 PSC Design Result Diagram